System for spectroscopy using an arbitrary dispersive element

ABSTRACT

Systems and methods for uses the inherent spectral dispersion of commercially available or easily fabricated diffusers to generate speckle patterns that are unique to each wave-length. In an embodiment, a computational spectrometer includes an arbitrary dispersive element (ADE); a detector configured to capture, as light passes through the ADE, a speckle pattern of transmitted dispersed light, unique for each spectrum; and an electronic processor coupled to the detector and configured to map the detected speckle pattern, received from the detector, to the input spectrum via a computational reconstruction algorithm, wherein the computational reconstruction algorithm is calibrated using a calibration data comprising a set of unique diffuse speckle patterns associated with each wavelength.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a non-provisional of and claims benefit of U.S. Provisional Patent Application No. 63/326,188, filed on Mar. 31, 2022, the entire contents of which are incorporated herein by reference.

BACKGROUND

Computational spectroscopy breaks the inherent one-to-one spatial-to-spectral pixel mapping of traditional spectrometers by multiplexing spectral data over a given sensor region. Most computational spectrometers require components that are complex to design, fabricate, or both.

SUMMARY

Traditional spectrometers use an optical element such as a grating or prism to linearly disperse a broadband optical signal into its constituent wavelength components. The resulting one-to-one spectral-to-spatial (camera pixel) mapping simplifies measurement of the amplitudes of the underlying spectral components. A major limitation of these spectrometers, however, is the inherent trade-off between bandwidth, dispersion angle (or system footprint), and spectral resolution, which leads to bulky designs with large footprints and expensive components.

Emerging alternative spectrometer designs leverage the power of computational optics to reconstruct spectra from disordered spatial patterns in one and two dimensions. These systems replace the one-to-one spectral-to-spatial coding of a traditional spectrometer with a spectral multiplexing element and use computational algorithms to reconstruct the spectrum of interest. Such computational spectrometers have been demonstrated using coded-apertures, integrated photonics, photonic crystal filters, and custom diffractive elements. However, the dispersive elements used in these systems are often complex to design, fabricate, or both.

Recent computational spectrometers using speckle correlation patterns resulting from multimode fibers (MMF), disordered alumina substrates, and frosted glass substrates demonstrate the potential utility of off-the-shelf, low-cost components for computational spectroscopy.

Accordingly, embodiments of the present disclosure are generally directed to systems that employ a free-space, scattering-based computational spectrometer using an extremely low-cost diffuser (“DiffuserSpec”). More particularly, DiffuserSpec is a simple computational spectrometer that uses the inherent spectral dispersion of commercially available or easily fabricated diffusers to generate speckle patterns that are unique to each wave-length. Using tape (e.g., Scotch tape) as a diffuser, for example, narrowband and broadband spectral reconstructions with 2-nm spectral resolution over an 85-nm bandwidth in the near-infrared are demonstrated, limited only by the bandwidth of the calibration dataset.

Particular embodiments of the subject matter described in this disclosure can be implemented so as to realize one or more of the following advantages. DiffuserSpec provides a simple way to make computational spectroscopy more accessible and versatile to general research and commercial communities. The use of tape as the dispersive component in a simple computational spectrometer is able to reconstruct narrow and broadband spectra with better resolution than other works that leverage coded-aperture detection (3.6 nm), custom diffractive elements (2 nm), and frosted glass (4.25 nm). The DiffuserSpec strategy can be implemented with any arbitrary dispersive element (ADE), and the analysis can be generalized to determine the expected resolution and performance of any ADE. Some advantages of DiffuserSpec over traditional spectrometers include: (1) ADEs can be obtained at extremely low cost; (2) the system bandwidth can be tuned by changing the calibration dataset and not the system footprint, enabling compact designs with broadband performance. Although the DiffuserSpec is insensitive to alignment during setup, the resulting reconstruction is highly sensitive to the spatial-spectral transfer matrix (SSTM) obtained during calibration; hence, the input source, ADE, and sensor can be rigidly attached. This alignment is sufficiently stable to enable use of the same SSTM to accurately reconstruct desired spectra over multiple days. It is also possible that changes to the optical setup may improve the performance, such as angling the detector or pixel binning.

In one aspect, disclosed herein, are computational spectrometers. These spectrometers includes an ADE, a detector, and an electronic processor coupled to the detector. The detector is configured to capture, as light passes through the ADE, a speckle pattern of transmitted dispersed light, unique for each spectrum. The electronic processor is configured to map the detected speckle pattern, received from the detector, to the input spectrum via a computational reconstruction algorithm. The computational reconstruction algorithm is calibrated using a calibration data comprising a set of unique diffuse speckle patterns associated with each wavelength. In some embodiments, the calibration data is organized into a SSTM. In some embodiments, the computational reconstruction algorithm uses spatial-spectral multiplexing to yield a compact system. In some embodiments, the ADE is tape. In some embodiments, the tape is transmissive and dispersive. In some embodiments, the tape is pressure-sensitive or adhesive tape. In some embodiments, the ADE, when illuminated, produces the diffuse speckle pattern as a function of an illumination wavelength and the ADE's random refractive surface.

It is appreciated that methods in accordance with the present disclosure can include any combination of the aspects and features described herein. That is, methods in accordance with the present disclosure are not limited to the combinations of aspects and features specifically described herein, but also may include any combination of the aspects and features provided.

The details of one or more implementations of the present disclosure are set forth in the accompanying drawings and the description below. Other features and advantages of the present disclosure will be apparent from the description and drawings, and from the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

A better understanding of the features and advantages of the present subject matter will be obtained by reference to the following detailed description that sets forth illustrative embodiments and the accompanying drawings of which:

FIG. 1A depicts an example of a traditional grating-based system;

FIG. 1B depicts an example of the described DiffuserSpec system;

FIG. 1C depicts an example of the general operating principles employed with in the described DiffuserSpec system;

FIG. 1D depicts a representative speckle patterns resulting from monochromatic illumination of the DiffuserSpec with collimated light;

FIG. 1E depicts another representative speckle patterns resulting from monochromatic illumination of the DiffuserSpec with collimated light;

FIG. 1F depicts an overlay of two sub-regions of the full speckle pattern that have been magnified to show the variation of the speckle distribution between the two wavelengths;

FIG. 2A depicts a chart that shows representative reconstruction results for six narrowband spectra overlaid on the same graph;

FIG. 2B depicts a chart that shows two-peak reconstruction of a 2-nm separation measured using the same SSTM data;

FIG. 3A depicts a visual representation of wavelengths for each individual pixel in the sensor array;

FIG. 3B plots the resolution versus lateral dispersion angle taken from the dotted white line in FIG. 3A;

FIG. 3C depicts a normalized spectral correlation function for different sampling masks;

FIG. 3D depicts a normalized single-peak reconstructions for each sampling scheme;

FIG. 4A depicts a modulated version of the source spectrum for a broadband spectral reconstruction with a tape diffuser; and

FIG. 4B depicts an alternate SLD source spectrum for a broadband spectral reconstruction with a tape diffuser;

FIG. 5 depicts an example system that includes a computer or computing device that can be programmed or otherwise configured to implement systems or methods of the present disclosure.

DETAILED DESCRIPTION

Before any embodiments of the disclosure are explained in detail, it is to be understood that the disclosure is not limited in its application to the details of embodiment and the arrangement of components set forth in the following description or illustrated in the following drawings. The disclosure is capable of other embodiments and of being practiced or of being carried out in various ways. Also, it is to be understood that the phraseology and terminology used herein is for the purpose of description and should not be regarded as limiting. The use of “including,” “comprising” or “having” and variations thereof herein is meant to encompass the items listed thereafter and equivalents thereof as well as additional items. The terms “mounted,” “connected” and “coupled” are used broadly and encompass both direct and indirect mounting, connecting and coupling. Further, “connected” and “coupled” are not restricted to physical or mechanical connections or couplings, and can include electrical or hydraulic connections or couplings, whether direct or indirect.

Embodiments of the present disclosure are generally a computational spectrometer that includes an ADE; a detector configured to capture, as light passes through the ADE, a speckle pattern of transmitted dispersed light, unique for each spectrum; and an electronic processor coupled to the detector and configured to map the detected speckle pattern, received from the detector, to the input spectrum via a computational reconstruction algorithm. In some embodiments, the computational reconstruction algorithm is calibrated using a calibration data comprising a set of unique diffuse speckle patterns associated with each wavelength.

Definitions

Unless otherwise defined, all technical terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which the present subject matter belongs. As used in this specification and the appended claims, the singular forms “a,” “an,” and “the” include plural references unless the context clearly dictates otherwise. Any reference to “or” herein is intended to encompass “and/or” unless otherwise stated.

As used herein, the term “about” or “approximately” as applied to one or more values of interest, refers to a value that is similar to a stated reference value, or within an acceptable error range for the particular value as determined by one of ordinary skill in the art, which will depend in part on how the value is measured or determined, such as the limitations of the measurement system. The term “approximately” as used herein refers to any values, including both integers and fractional components that are within a variation of up to ±10% of the value modified by the term “about.” In certain aspects, the term “approximately” refers to a range of values that fall within 20%, 19%, 18%, 17%, 16%, 15%, 14%, 13%, 12%, 11%, 10%, 9%, 8%, 7%, 6%, 5%, 4%, 3%, 2%, 1%, or less in either direction (greater than or less than) of the stated reference value unless otherwise stated or otherwise evident from the context (except where such number would exceed 100% of a possible value). Alternatively, “approximately” can mean within 3 or more than 3 standard deviations, per the practice in the art. Alternatively, such as with respect to biological systems or processes, the term “about” can mean within an order of magnitude, in some embodiments within 5-fold, and in some embodiments within 2-fold, of a value.

Overview

Described herein is a system that employ a free-space, scattering-based computational spectrometer using a low-cost diffuser. In some embodiments, the diffuser employed is tape. In some embodiments, the diffuser is a pressure-sensitive or adhesive tape (e.g., 3M Scotch Magic Tape) that will stick with application of pressure, without the need for a solvent (such as water) or heat for activation. These tapes generally include the tape itself, which often is cellophane, cellulose acetate, or polyvinyl chloride (other materials include paper, plastic film, cloth, or metal foil coated onto a backing material such as paper, plastic film, cloth, or metal foil), a pressure-sensitive adhesive, and a release liner, which keeps the tape from sticking to itself. Tape is an exceedingly cheap, practical alternative to custom-designed optics and gratings and has been previously used for computational imaging. When illuminated, the tape produces a diffuse speckle pattern that is a function of the illumination wavelength and the tape's random refractive surface. In some embodiments, the tape diffuser can enable spectroscopy of narrowband and broadband spectra. The cost-effective design of DiffuserSpec highlights the potential of commercially available dispersive components to serve as new options for the construction of low-cost, compact spectrometers for scientific applications across a range of disciplines. The DiffuserSpec strategy, moreover, showcases the benefit of using computation to replace costly, sophisticated optical components.

In contrast with a traditional grating-based system (shown in FIG. 1A), DiffuserSpec (shown in FIG. 1B) takes advantage of spatial-spectral multiplexing to yield a more compact system. FIG. 1C shows the general operating principles employed. First, light passes through an ADE such as Scotch tape. Next, the pattern of transmitted dispersed light, unique for each spectrum, is captured by a detector. A detector includes a camera or any pixelated electronic device that can receive data from multiple samples at once. A computational reconstruction algorithm (e.g., linear inversion) then maps the detected speckle pattern to the input spectrum, using data obtained during a calibration step. In some embodiments, the calibration data, organized into the SSTM, comprises the set of unique diffuse speckle patterns associated with each wavelength. FIGS. 1D and 1E each show a representative speckle patterns resulting from monochromatic illumination of the DiffuserSpec with collimated light (4-mm beam diameter) at 818 nm and 828 nm set 15 mm from a Scotch tape diffuser, which was placed 50 mm from a scientific CMOS (sCMOS) sensor (PCO Edge 5.5). FIG. 1F shows an overlay of two sub-regions of the full speckle pattern that have been magnified to show the variation of the speckle distribution between the two wavelengths.

Although the detected speckle patterns appear random, they are largely deterministic. The measurement on the 2D sensor, b(x,y), is approximately a weighted sum of the components of the SSTM, A(x,y,λ). The weights w(λ) define the input spectrum:

$\begin{matrix} {{b\left( {x,y} \right)} = {\int{\text{?}{A\left( {x,y,\lambda} \right)}{w(\lambda)}d{\lambda.}}}} & (1) \end{matrix}$ ?indicates text missing or illegible when filed

In the case of a finite SSTM calibrated at discrete wavelengths, this expression can be mathematically rewritten as a linear system of equations; however, a more accurate expression should include the effect of noise terms, which may arise from sources including photon shot noise in the source light, dark noise in the detector, or small perturbations or misalignments of the optics:

b=Aw+n.  (2)

Here, b=b(x,y) is a matrix containing the sensor pixel measurements, w=w(λ) is a vector that describes the input spectrum weights as applied to A=A(x,y,λ), and n=n(x,y) describes the noise at each pixel.

Ideally, the solution for w may be obtained using a simple reconstruction algorithm: the linear inverse of A. That is, w=A⁻¹ b; however, the presence of noise leads to ill-conditioning and overdetermination of the system. Inverting an ill-conditioned linear system will cause any noise components along the vectors associated with small singular values to become greatly amplified. Thus, our reconstruction attempts to find the least-squares solution,

$\begin{matrix} {{\hat{w} = {\arg\underset{\text{w≥0}}{\min}{❘{{Aw} - b}❘}_{2}^{2}}},} & (3) \end{matrix}$

using a low-rank inverse:

ŵ=Â ⁻¹ b.  (4)

Where Â⁻¹ may be computed by performing the singular value decomposition (SVD) of A, inverting its singular values, and using a filter to attenuate the inverted singular values that exceed an empirically determined threshold:

Â ⁻¹ =V(F _(σ)Σ⁻¹)U ^(T).  (5)

Here, Σ is a diagonal matrix containing the singular values of A from largest to smallest, and U and V contain the corresponding singular vectors. Additionally, F_(σ) represents the filter on the inverted singular values. In some embodiments, a half-Gaussian filter was employed to smooth the inverted singular values with a tuning parameter, σ, corresponding to the Gaussian filter width. The value of σ used affects the noisiness and performance of the reconstruction and was chosen empirically to minimize error between the ground truth and DiffuserSpec spectra. Additionally, in this embodiment, a non-negativity condition was enforced to the reconstructions by setting negative values to 0. Overall, this method is similar to a truncated SVD algorithm that uses a hard threshold on the singular values. In some embodiments, applying a hard threshold caused ripple artifacts in the reconstructed spectrum that a smoother (Gaussian) filter avoided.

In one example, to demonstrate the use of DiffuserSpec for spectroscopy, the SSTM A of the ADE, Scotch tape, was measured during a calibration step using a broadband superluminescent diode (SLD) source (Superlum, Broadlighter) connected to a custom-built monochromator with a spectral resolution of 0.1 nm. A 90:10 fiber coupler was used to simultaneously direct light from the monochromator to both the DiffuserSpec and a commercial spectrometer (Thorlabs, CCS175) was measured. In this way, the ground-truth spectrum associated with each speckle pattern was obtained. Moreover, automated software in LabView was developed to expedite the calibration procedure. An SSTM comprising an average of 10 frames (75-ms each) at each of 344 monochromatic wavelengths spanning 784.7-870.4 nm (0.25-nm step size) was collected. The sampling density was chosen based on preliminary measurements carried out to ensure the spectral resolution of the DiffuserSpec was limited by the spectral dispersion of the ADE rather than the calibration matrix. To account for power differences associated with different wavelengths from the monochromator, the speckle pattern for each wavelength was normalized to have an equal total intensity. The normalization was used to remove the influence of the intensity profile of the calibration source on future reconstructions.

Using the full 3D SSTM (2560 pix 2160 pix 344 frames) for reconstruction by SVD resulted in an overdetermined inverse problem and required excessive computational resources. Hence, the dimensionality of the problem was reduced by sampling a subset of the pixels from each frame prior to computing A to yield a 2D SSTM of size P×S, where P is the number of pixels in the subset and S is the number of calibration frames. The SSTM and the sensor measurement, b (size P 1, sub-sampled at the same pixels as used for A), were then used to determine w by solving the inverse problem. Note that while the reconstruction algorithm is agnostic to the order of vectorized pixel data within the SSTM, the subset of pixels used is highly relevant for determining the quality of the reconstruction.

FIG. 2A shows representative reconstruction results for six narrowband spectra overlaid on the same graph. The depicted reconstruction of six narrowband spectral peaks were acquired separately, where the black, dashed lines correspond to the illumination wavelengths. The wavelengths used for reconstruction were not included in the SSTM, which was down-sampled by omitting every evenly indexed spectral column (i.e., S=172). That is, the wavelengths used for b in the inverse problem were selected from the omitted spectral data. In this example, A and b were sub-sampled by selecting a random distribution of P=40,000 pixels from the full 2650×2160 SSTM frame, resulting in a 2D SSTM sized 40,000×172 (spatial spectral) pixels. In some embodiments, DiffuserSpec reconstructs the individual wavelength peaks across a broad bandwidth with good resolution, although the full width at half maximum resolution of the reconstructed peaks is worse than the resolution of the monochromator (1.25 nm versus 0.1 nm). The ability of DiffuserSpec to reconstruct a two-peak spectrum was tested by collecting speckle patterns from two monochromatic peaks sequentially and averaging them together. Simulating data in this way is reasonable because light at two different wavelengths does not interfere; hence, the intensity patterns can be added. FIG. 2B shows that the reconstruction can resolve a 2-nm separation measured using the same SSTM data. For both, σ=250 pix.

In some embodiments, the performance of a given ADE for spectroscopy is related to the spectral correlation of the wavelength-dependent speckle patterns it generates. Specifically, the spectral correlation function, C, can be used to assess the degree of correlation between the speckle patterns associated with two wavelengths separated by a difference δλ (i.e., a spectral shift):

$\begin{matrix} {{C\left( {p,{\delta\lambda}} \right)} = {\frac{\left. {< {{A\left( {p,\lambda} \right)}*{A\left( {p,{\lambda + {\delta\lambda}}} \right)}}} \right) >}{\left\langle {A\left( {p,\lambda} \right)} \right\rangle*\left\langle {A\left( {p,{\lambda + {\delta\lambda}}} \right)} \right\rangle} - 1.}} & (6) \end{matrix}$

Here, p represents the pixel used for the calculation, A is the intensity of light measured at pixel p, and <.> represents a mean operator over wavelength. Typically, the value C(δλ) is obtained by averaging C(p, δλ) across all pixels used in the reconstruction. The resulting plot may then be used to estimate the spectral resolution, which can be defined as the spectral shift at which C(δλ) drops to half of its maximum value. For the data used in FIG. 2B, this value was 2 nm and is consistent with our ability to resolve the two peaks. Notably, the resolution of the two-peak reconstruction differs from that of single-peak reconstructions.

As stated previously, the full 3D SSTM contains a large amount of data, which can place a significant computational burden on performing the reconstruction. One solution to this problem is to reduce the amount of total data by using only subset of P pixels in each frame, but the choice of which subset of pixels to use will affect the spectrometer performance. To investigate the impact of pixel choice on resolution performance, the effects of different pixel regions on the resulting spectral correlations and the resolution of the reconstructions were analyzed.

FIG. 3A shows a visual representation of λ_(res) for each individual pixel in the sensor array, which relates to the contribution of a given pixel to the resolution of the final reconstruction. Here, the raw 2D heatmap has been smoothed (using a 50-pixel Gaussian filter) to illustrate the general trend: pixels near the edge of the field-of-view (FOV) show more spectral decorrelation than pixels near the center, which suggests that reconstructions that include pixels from edge regions should be capable of achieving higher resolution. This trend makes intuitive sense because the spectral dispersion of the light reaching the outer edges of the FOV is more significant than that of light toward the central FOV, similar to higher orders of a grating. FIG. 3B plots the resolution versus lateral dispersion angle taken from the dotted white line in FIG. 3A. The FWHM(2.35°) is a measure of the angular spectral dispersion, which is characteristic for a given diffuser and is a measure of its utility for spectroscopy.

To illustrate the impact of pixel choice on the reconstruction, three binary masks were used to select for pixels associated with low or high values of λ_(res). To control for the number of pixels used in the reconstruction, the same number (P=40,000) of pixels was randomly sampled from the white region of each mask. The choice of 40,000 (˜0.7% of the data) represents a balance of computational ease and sufficiently high sampling density to produce similar reconstruction patterns over multiple iterations of random selection (i.e., an error within the noise floor).

FIG. 3C shows the normalized spectral correlation function for different sampling masks, shown as insets. The depicted spectral correlation plots were generated by applying Eq. (6) to the pixel subsets extracted from each mask [FIG. 3(c) insets] and normalizing to the maximum value of C in each case. The black “x” at 0.5 indicates the half-maximum value used to determine λ_(res), or the estimated resolution for that pixel subset. Sampled pixels were chosen randomly from within the white areas. As expected, λ_(res) significantly better (smaller) when using pixels from the “outer” parts of the FOV rather than the “inner” parts of the FOV (λ_(res)=2.1 nm versus 5 nm). The resolution is even better (λ_(res)=1.55 nm) when selecting pixels from the “corners” of the FOV. These results make sense because Eq. (6) is merely an average of the values of C(δλ) for all pixels in the subset. The single-peak reconstructions in FIG. 3D corroborate this trend, suggesting that the resolution of the resulting reconstruction depends on which pixels are used. Notably, the actual FWHM resolution of the single peak is better than the prediction from C [1.23 nm (corners), 1.4 nm (outer circle), and 2.03 nm (inner circle)], suggesting that λ_(res) is not synonymous with the resolution; as with other computational spectrometers, the reconstruction performance is also a function of the algorithm and other parameters used (e.g., σ).

To explore the ability of the DiffuserSpec to reconstruct broadband spectra, two signals were analyzed. The first was a modulated version of the source spectrum created by placing a physical mask in the optical path of the monochrometer, and the second was the spectrum of a broadband SLD source (Inphenix) (λ₀ 850 nm, λ_(FWHM) 45 nm). FIG. 4 shows the ground-truth and DiffuserSpec spectra for each case using the “corners” mask sampling pattern from FIG. 3 . Each reconstruction has been normalized to its maximum value.

In FIG. 4A, the reconstruction shows good correlation with the two peaks at 824 nm and 840 nm. For FIG. 4B, the noise floor is higher for the reconstructed spectrum, and its intensity shows a sharp increase at the tail end of the calibration bandwidth, near 870 nm. The bandwidth mismatch between the calibration range and spectral range of the source may be a contributing factor to this error. Since the SSTM and reconstruction algorithm cannot extrapolate data for wavelengths longer than 870 nm, in some embodiments, the algorithm attributes these wavelength intensities to the next closest value within the calibration. In essence, non-calibrated wavelength information can be understood as components of the noise term presented in Eq. (2), which increase the uncertainty and error of the inverse solution. It is possible that these errors may be minimized using a more sophisticated reconstruction algorithm. The difference in the noise floor between the ground truth and the reconstructed spectrum may be derived from the noise characteristic of the source itself: as the source used was different from the source used to generate the SSTM for the reconstruction, it is likely the noise floor of the SSTM depends on the source used. Overall, these results suggest that DiffuserSpec can reconstruct broadband data, and that the reconstruction depends as well on the calibration range and the noise level of the calibration dataset.

FIG. 5 depicts an example system 500 that includes a computer or computing device 510 that can be programmed or otherwise configured to implement systems or methods of the present disclosure. In the depicted embodiment, the computer or computing device 510 includes an electronic processor (also “processor” and “computer processor” herein) 512, which is optionally a single core, a multi core processor, or a plurality of processors for parallel processing. The depicted embodiment also includes memory 517 (e.g., random-access memory, read-only memory, flash memory), electronic storage unit 514 (e.g., hard disk or flash), communication interface 515 (e.g., a network adapter or modem) for communicating with one or more other systems, and peripheral devices 516, such as cache, other memory, data storage, microphones, speakers, etc. In some embodiments, the memory 517, storage unit 514, communication interface 515 and peripheral devices 516 are in communication with the electronic processor 512 through a communication bus (shown as solid lines), such as a motherboard. In some embodiments, the bus of the computing device 510 includes multiple buses. In some embodiments, the computing device 510 includes more or fewer components than those illustrated in FIG. 5 and performs functions other than those described herein.

In some embodiments, the memory 517 and storage unit 514 include one or more physical apparatuses used to store data or programs on a temporary or permanent basis. In some embodiments, the memory 517 is volatile memory and requires power to maintain stored information. In some embodiments, the storage unit 514 is non-volatile memory and retains stored information when the computer is not powered. In further embodiments, memory 517 or storage unit 514 is a combination of devices such as those disclosed herein. In some embodiments, memory 517 or storage unit 514 is distributed across multiple machines such as a network-based memory or memory in multiple machines performing the operations of the computing device 510.

In some cases, the storage unit 514 is a data storage unit or data store for storing data. In some instances, the storage unit 514 store files, such as drivers, libraries, and saved programs. In some embodiments, the storage unit 514 stores user data (e.g., user preferences and user programs). In some embodiments, the computing device 510 includes one or more additional data storage units that are external, such as located on a remote server that is in communication through an intranet or the internet.

In some embodiments, methods as described herein are implemented by way of machine or computer executable code stored on an electronic storage location of the computing device 510, such as, for example, on the memory 517 or the storage unit 514. In some embodiments, the electronic processor 512 is configured to execute the code. In some embodiments, the machine executable or machine-readable code is provided in the form of software. In some examples, during use, the code is executed by the electronic processor 512. In some cases, the code is retrieved from the storage unit 514 and stored on the memory 517 for ready access by the electronic processor 512. In some situations, the storage unit 514 is precluded, and machine-executable instructions are stored on the memory 517.

Examples of operations performed by the electronic processor 512 can include fetch, decode, execute, and write back. In some cases, the electronic processor 512 is a component of a circuit, such as an integrated circuit. One or more other components of the computing device 510 can be optionally included in the circuit. In some cases, the circuit is an application specific integrated circuit (ASIC) or a field programmable gate arrays (FPGAs). In some cases, the operations of the electronic processor 512 can be distributed across multiple machines (where individual machines can have one or more processors) that can be coupled directly or across a network.

In some cases, the computing device 510 is optionally operatively coupled to a communication network via the communication interface 515. In some cases, the computing device 510 communicates with one or more remote computer systems through the network. In some cases, a user can access the computing device 510 via the network. In some cases, the computing device 510 is configured as a node within a peer-to-peer network.

In some cases, the computing device 510 includes or is in communication with one or more output devices 520. In some cases, the output device 520 includes a display to send visual information to a user. In some cases, the output device 520 is a liquid crystal display (LCD). In other cases, the output device 520 is a thin film transistor liquid crystal display (TFT-LCD) or an organic light emitting diode (OLED) display. In some cases, the output device 520 is a touch sensitive display that combines a display with a touch sensitive element that is operable to sense touch inputs as and functions as both the output device 520 and the input device 530. In still further cases, the output device 520 is a combination of devices such as those disclosed herein. In some cases, the output device 520 displays a user interface (UI) 525 generated by the computing device (for example, software executed by the computing device 510).

In some cases, the computing device 510 includes or is in communication with one or more input devices 530 that are configured to receive information from a user. In some cases, the input device 530 is a keyboard. In some cases, the input device 530 is a keypad (e.g., a telephone-based keypad). In some cases, the input device 530 is a cursor-control device including, by way of non-limiting examples, a mouse, trackball, track pad, joystick, game controller, or stylus. In some cases, as described above, the input device 530 is a touchscreen or a multi-touchscreen. In other cases, the input device 530 is a microphone to capture voice or other sound input. In other cases, the input device 530 is a camera or video camera. In still further cases, the input device is a combination of devices such as those disclosed herein.

In some cases, the computing device 510 includes an operating system configured to perform executable instructions. The operating system is, for example, software, including programs and data that manages the device's hardware and provides services for execution of applications.

It should also be noted that a plurality of hardware and software-based devices, as well as a plurality of different structural components may be used to implement the described examples. In addition, embodiments may include hardware, software, and electronic components or modules that, for purposes of discussion, may be illustrated and described as if most of the components were implemented solely in hardware. In some embodiments, the electronic based aspects of the disclosure may be implemented in software (e.g., stored on non-transitory computer-readable medium) executable by one or more processors, such as electronic processor 512. As such, it should be noted that a plurality of hardware and software-based devices, as well as a plurality of different structural components may be employed to implement various embodiments. It should also be understood that although certain drawings illustrate hardware and software located within particular devices, these depictions are for illustrative purposes only. In some embodiments, the illustrated components may be combined or divided into separate software, firmware, or hardware. For example, instead of being located within and performed by a single electronic processor, logic and processing may be distributed among multiple electronic processors. Regardless of how they are combined or divided, hardware and software components may be located on the same computing device or may be distributed among different computing devices connected by one or more networks or other suitable communication links.

While preferred embodiments of the present disclosure have been shown and described herein, it will be obvious to those skilled in the art that such embodiments are provided by way of example only. Numerous variations, changes, and substitutions will now occur to those skilled in the art without departing from the described system. It should be understood that various alternatives to the embodiments described herein may be employed in practicing the described system.

Particular implementations of the subject matter have been described. Other implementations, alterations, and permutations of the described implementations are within the scope of the following claims as will be apparent to those skilled in the art. While operations are depicted in the drawings or claims in a particular order, this should not be understood as requiring that such operations be performed in the particular order shown or in sequential order, or that all illustrated operations be performed (some operations may be considered optional), to achieve desirable results.

Moreover, the separation or integration of various system modules and components in the implementations described earlier should not be understood as requiring such separation or integration in all implementations, and it should be understood that the described components and systems can generally be integrated together in a single product or packaged into multiple products. Accordingly, the earlier description of example embodiments does not define or constrain this disclosure. Other changes, substitutions, and alterations are also possible without departing from the spirit and scope of this disclosure. 

What is claimed is:
 1. A computational spectrometer comprising: an arbitrary dispersive element (ADE); a detector configured to capture, as light passes through the ADE, a speckle pattern of transmitted dispersed light, unique for each spectrum; and an electronic processor coupled to the detector and configured to map the detected speckle pattern, received from the detector, to the input spectrum via a computational reconstruction algorithm, wherein the computational reconstruction algorithm is calibrated using a calibration data comprising a set of unique diffuse speckle patterns associated with each wavelength.
 2. The computational spectrometer of claim 1, wherein the calibration data is organized into a spatial-spectral transfer matrix (SSTM).
 3. The computational spectrometer of claim 1, wherein the computational reconstruction algorithm uses spatial-spectral multiplexing to yield a compact system.
 4. The computational spectrometer of claim 1, wherein the ADE comprises tape.
 5. The computational spectrometer of claim 4, wherein the tape is transmissive and dispersive.
 6. The computational spectrometer of claim 4, wherein the tape is pressure-sensitive tape or adhesive tape.
 7. The computational spectrometer of claim 1, wherein, the ADE, when illuminated, produces the diffuse speckle pattern as a function of an illumination wavelength and the ADE's random refractive surface. 